- Email: [email protected]
A hybrid method of modified NSGA-II and TOPSIS to optimize performance and emissions of a diesel engine using biodiesel
Applied Thermal Engineering 59 (2013) 309e315
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
A hybrid method of modified NSGA-II and TOPSIS to optimize performance and emissions of a diesel engine using biodiesel Mir Majid Etghani a, *, Mohammad Hassan Shojaeefard b, Abolfazl Khalkhali b, Mostafa Akbari b a b
Mechanical Engineering Department, Islamic Azad University, Qaemshahr Branch, Mazandaran, Iran Automotive Engineering Department, Iran University of Science and Technology, Tehran, Iran
h i g h l i g h t s Effects of castor oil biodiesel blends have been examined on the diesel engine performance and emissions. Modeling engine performance and emissions by artificial neural network with back-propagation algorithm accurately. 2 and 6-objective optimization has been applied by the modified NSGA-II. Trade-off optimum design points are determined by applying TOPSIS.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 September 2012 Accepted 24 May 2013 Available online 3 June 2013
This paper addresses artificial neural network (ANN) modeling followed by multi-objective optimization process to determine optimum biodiesel blends and speed ranges of a diesel engine fueled with castor oil biodiesel (COB) blends. First, an ANN model was developed based on standard back-propagation algorithm to model and predict brake power, brake specific fuel consumption (BSFC) and the emissions of engine. In this way, multi-layer perception (MLP) network was used for non-linear mapping between the input and output parameters. Second, modified NSGA-II by incorporating diversity preserving mechanism called the ε-elimination algorithm was used for multi-objective optimization process. Six objectives, maximization of brake power and minimization of BSFC, PM, NOx, CO and CO2 were simultaneously considered in this step. Optimization procedure resulted in creating of non-dominated optimal points which gave an insight on the best operating conditions of the engine. Third, an approach based on TOPSIS method was used for finding the best compromise solution from the obtained set of Pareto solutions. 2013 Elsevier Ltd. All rights reserved.
Keywords: Performance Emissions Castor oil biodiesel ANN NSGA-II TOPSIS
1. Introduction Today caused by considerable growth of demands, known petroleum reserves are extremely diminishing and due to the environmental concerns for pollution from exhausted gases and demanding of greenhouse gas reduction, renewable and alternative fuels in the automotive fuel markets grew fast during the 21st century [1]. Since biodiesel has all the characteristics that an alternative fuel to petrodiesel should have such as technically feasible, economically competitive, environmentally acceptable, and easily available,
* Corresponding author. Tel.: þ98 9122393445; fax: þ98 2177240362. E-mail addresses: [email protected], [email protected] (M.M. Etghani), [email protected] (M.H. Shojaeefard), [email protected] (A. Khalkhali), [email protected] (M. Akbari). 1359-4311/$ e see front matter 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.05.041
therefore in the diesel engines, biodiesel is the best candidate as alternative for petroleum-based diesel fuels. Biodiesel is briefly defined as the monoalkyl esters of vegetable oils or animal fats. Biodiesel is an ecological, renewable and less polluting fuel, and therefore it is environmentally useful [2]. The usage of biodiesel does not require any changes in the fuel distribution infrastructure, and it is competitive with conventional diesel fuel. Furthermore, biodiesel biodegrades much more rapidly than diesel fuel. So, considerable environmental benefits are provided [3]. Because of experimentally determining the engine performance map for different operating conditions and biodiesel blends are time and money consuming, ANNs are used in recent studies. ANN as a computational modeling tool is employed widely to alleviate the burden of experimental testing. Recently, the application of ANN method to predict performance and emissions of internal combustion engines has gained significant success. Ghobadian et al. [4] modeled a diesel engine using waste cooking biodiesel fuel by
310
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
ANN. They considered engine speed, percentage of bio-fuel blend as the input variables and torque, BSFC, Hydrocarbon (HC) and Carbone Monoxide (CO) as the outputs. Kiani Deh Kiani et al. [5] used ANN to predict the performance and emissions from a spark ignition engine using ethanol-gasoline blends where they considered engine speed, engine speed and blend percentage as the input parameters and engine torque, power and exhaust emissions (CO, CO2, NOx and HC) of the engine as the output parameters. Kara Togun et al. [6] developed ANN to predict torque and BSFC of a gasoline engine in terms of spark advance, throttle position and engine speed. Shivakumar et al. [7] have used ANN for prediction of performance and emission characteristics of a CI engine using WCO. In their work, ANN modeling was used to predict BTE, BSEC, Texh, NOx, HC and Smoke. This technology was also used for modeling of valve timing in a SI engine [8]. Design of modern engines is driven by many competing criteria. Reduction of brake specific fuel consumption is common in the automotive industry to reduce the fuel consumption. Moreover, because of the environmental concerns, reduction of emissions is also significant. On the other hand, increasing the engine power is the important goal of engine designers. So, to consider all such criteria simultaneously, a complex multi-objective optimization problem (MOP) must be solved. Many different methods were proposed by previous researchers for solving MOPs [9,10]. Nondominated Sorting Genetic Algorithm (NSGA-II) proposed by Srinivas and Deb [11], which is Pareto based approaches is one of the efficient algorithms for solving MOPs. It generates a set of nondominated solutions (Pareto solutions), where a non-dominated solution performs better on at least one criterion than the other solutions. To improve NSGA-II, Nariman-Zadeh proposed modified NSGA-II which use ε-elimination algorithm rather than crowding factor [12]. This method is employed successfully in many recent studies [13,14]. After finding out the non-dominated points, it is desired to find some trade-off optimum points compromising objective functions. For this purpose, technique for ordering preferences by similarity to ideal solution (TOPSIS) can be used. TOPSIS is based on simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. Several numerical experiments show that NSGA-II determines the Pareto set and TOPSIS finds the best compromise solutions for different scenarios [15,16]. In the present study, optimal operating condition of a diesel engine fueled by biodiesel is extracted by an approach based on three steps. At the first step, a multi-layer perception (MLP) network is learned by experimental data to model and predict engine power, BSFC and emissions. Such ANN models are then employed in the multi-objective optimization process at the second step. In this way, modified NSGA-II by incorporating diversity preserving mechanism called the ε-elimination algorithm is used to
Table 1 Engine technical specifications. Bore stroke Number of cylinders Volume capacity Cycle Aspiration Combustion system Compression ration Max. power Fuel pump Governing Cooling Weight Length width height
100 mm 127 mm 4 3.99 L 4 Stroke Wastegated turbocharger Fast ram direct injection 17.25:1 61 kW in 2000 rpm Bosch rotary with Boost control Mechanical Water, belt driven water pump 265 Kg 678.7 mm 655 mm 748.5 mm
Fig. 1. Schematic diagram of experimental setup.
set up a multi-objective optimization framework for maximizing engine power, minimizing BSFC and emissions. At the last step, TOPSIS is used to find the best compromise solution. 2. Experimental methodology The experiments were performed on the agricultural direct injection compression engine with specifications given in Table 1. An eddy current dynamometer was used for gathering outputs of engine. The schematically prepared diagram of experimental setup is given in Fig. 1. The relative emission parameters from an online and accurately calibrated exhaust gas analyzer AVL DiCOM were recorded. The accuracies of the measured parameters and the uncertainties in the calculated parameters are given in Table 2. The experiments were carried out by using pure diesel, B5 (5% biodiesel þ 95% diesel), B10, B15, B20, B25 and B30 at full loads and various engine speeds (1200, 1400, 1600, 1700, 1800, 2000 rpm). All tests were completed without any modifications on the engine. The tests were carried out under steady-state condition. Before each test, the engine was warmed up with diesel fuel for about 15 min until the cooling water temperature was stabilized. Then brake power, BSFC, Nitrogen oxides (NOx), Carbone dioxide (CO2), CO and PM were measured. Each test was repeated three times and the results of the three repetitions were averaged. Some of the experimental results are reported in Table 3. 3. Modeling and prediction using artificial neural network (ANN) The main focus of this section is modeling and prediction of engine output using ANN based on experimental results. The backpropagation learning algorithm was used in feed forward with one hidden layer. Blend percentage and engine speed were considered
Table 2 The accuracies uncertainties in the results. Parameters
Accuracies
Load Speed Time CO CO2 NOx PM Calculated results Power BSFC
2 N.m 5 rpm 0.5% 0.01 % Vol 0.01 % Vol 1 ppm 1 mg/m3 Uncertainty 0.2% 0.22%
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315 Table 3 Samples of experimental results with input and output parameters. No.
1 2 6 7 10 11 12 25 26 27 28 29 30 37 38 39 40 41 42
Inputs
Outputs
Speed (rpm)
Blend (%)
Power (hp)
BSFC (g/kW-h)
PM (mg/m3)
NO (PPM)
CO (%)
CO2 (%)
1200 1400 2000 1200 1700 1800 2000 1200 1400 1600 1700 1800 2000 1200 1400 1600 1700 1800 2000
0 0 0 5 5 5 5 20 20 20 20 20 20 30 30 30 30 30 30
56 65 82 55 72 76.1 79.8 52 60 64.1 66.9 70.4 74.3 50.1 57.7 62.2 64 67.65 71.3
241.4 237.6 255.7 245.8 243.9 250.9 263.9 255.5 250.1 252.37 260.3 271.2 288.2 258.7 252.63 254.5 264.22 276.8 300.4
521.9 160.8 41.13 488.6 58.79 47.78 36.78 361 111 73.5 34.61 31.04 27.45 327 102 65.47 27.15 25.63 24.12
1380 1254 926 1396 1193 1081 970 1428 1364 1311 1258 1140 1022 1445 1409 1345 1281 1165 1050
0.43 0.37 0.31 0.42 0.322 0.312 0.302 0.32 0.29 0.28 0.27 0.262 0.255 0.28 0.27 0.265 0.26 0.25 0.24
12.4 11.4 8.9 12.2 9.7 9.1 8.5 11.5 9.1 8.5 8.15 7.9 7.64 10.8 8 7.49 7.38 7.3 7.21
as input layer components, while the Power, BSFC, PM, NOx, CO and CO2 were considered as output layer components of the ANNs. In the ANN model, 34 values of which 42 experiments were used for training the network and 8 values were selected randomly to test the performance of the trained network. The input layer neurons receive information from the outside environment and transmit them to the neurons of the hidden layer without performing any calculation. The hidden layer neurons then process the incoming information and extract useful features to reconstruct the mapping from the input space. The neighboring layers are fully interconnected by weights. Finally, the output layer neurons produce the network prediction to the outside world [17]. One of the most important tasks in ANN studies is to determine the optimal network architecture which is related to hidden layers and neurons in it. Generally, the trial-and-error approach is used. In this study, the best architecture of the network was obtained by trying different hidden layers and neurons. The trial started on hidden layer with ten neurons, and the performance of each network was checked by three standard criteria, R, RMSE and MAPE (R is the correlation coefficient, RMSE is the root mean square error, and MRE is the mean relative error). These criteria are defined as following equations respectively:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 ! P u u j tj oj R ¼ t1 P 2 j oj
¼
¼
ð1=pÞ
X 1=2 tj oj 2
! p 1 X tj oj 100 tj p 1
311
representing inputs, neurons in hidden layers, and outputs, respectively. Table 4 shows its criteria. The learning algorithm used in the study is LevenbergeMarquardt (LM), activation function is logistic sigmoid (logsig) transfer functions and epoch numbers is 20,000. 4. Multi-objective optimization Multi-objective optimization, which is also called multi criteria optimization or vector optimization, defined as finding a vector of decision variables satisfying constraints to give acceptable values to all objective functions [19,20]. In these problems, there are several objectives or cost functions (a vector of objectives) to be optimized (minimized or maximized) simultaneously. These objectives often conflict with each other so that improving one of them will deteriorate another. Thus, there is no single optimal solution as the best with respect to all the objective functions. Instead, there is a set of optimal solutions, known as Pareto optimal solutions or Pareto front [21e25] for multi-objective optimization problems. The concept of Pareto front or set of optimal solutions in the space of objective functions in MOPs stands for a set of solutions that are non-dominated to each other but are superior to the rest of solutions in the search space. This means that it is not possible to find a single solution to be superior to all other solutions with respect to all objectives so that changing the vector of design variables in such a Pareto front consisting of these non-dominated solutions could not lead to the improvement of all objectives simultaneously. Therefore, such a change will lead to deteriorating of at least one objective. Thus, each solution of the Pareto set includes at least one objective inferior to that of another solution in that Pareto set, although both are superior to others in the rest of search space. Such problems can be mathematically defined as: Find the vector X * ¼ ½x*1 ; x*2 ; .; x*n to optimize
FðXÞ ¼ ½f1 ðXÞ; f2 ðXÞ; .; fk ðXÞT
(4)
subject to m inequality constraints
gi ðXÞ 0;
i ¼ 1 to m
(5)
and p equality constraints
hj ðXÞ ¼ 0;
j ¼ 1 to p
(6)
(2)
where X * ˛
(3)
Table 4 Three standard criteria obtained from the ANN.
(1)
R
where t is the target value, o is the output value and p is the pattern number [18]. The goal is to maximize correlation coefficient to obtain a network with the best generalization. Many different network models were tried and their R, RMSE and MAPE values were calculated. Based on this analysis, the optimal architecture of the ANN was constructed as 2e15e6 neural network architecture
Power BSFC PM NOx CO CO2
RMSE
MAPE
Train
Test
Train
Test
Train
Test
0.999995 0.999998 0.999995 0.999996 0.999978 0.999983
0.999956 0.999957 0.996709 0.999955 0.999937 0.999931
0.000772 0.001158 0.000719 0.001303 0.001472 0.001968
0.002223 0.0047 0.008131 0.004254 0.002437 0.003807
0.216595 0.12151 0.733854 0.169048 0.396388 0.350319
0.532047 0.51145 4.15107 0.538951 0.664076 0.685741
312
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
ci ¼ f1; 2; .; kg, ui vi ^ dj˛f1; 2; .; kg : ui < vi. In other words, there is at least one uj which is smaller than vj whilst the remaining u’s are either smaller or equal to corresponding v’s. A point X * ˛U (U is a feasible region in
Fig. 2. BSFC vs. power in six-objective optimization.
Fig. 3. NOx vs. power in six-objective optimization.
objective weights. The TOPSIS process for determining the best compromise solution is briefly presented as follows: 1) Input matrix S, where the element sij is the jth objective value of the ith alternative (that is, S is composed of the Pareto solutions) 2) Calculate normalized rating ~sij according to the following equation:
sij ~sij ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pm 2ffi i¼1 sij
i ¼ 1; .; m; j ¼ 1; .; n
(7)
3) Construct the weighted normalized values bs ij using the following equation:
b s ij ¼ wj ~sij
i ¼ 1; .; m; j ¼ 1; .; n
(8)
where wj is the weight value of jth attribute and must satisfy: n X
wj ¼ 1
(9)
j¼1
4) Determine Sþ and S as follow:
Sþ ¼ S ¼
maxb s ij jj˛J1 ; minb s ij jj˛J2 ;
i ¼ 1; 2; .; m
(10)
minb s ij jj˛J1 ; maxb s ij jj˛J2 ;
i ¼ 1; 2; .; m
(11)
Fig. 4. PM vs. power in six-objective optimization.
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
313
Fig. 5. CO vs. power in six-objective optimization.
Fig. 7. PM vs. BSFC in six-objective optimization.
where J1 is a set of benefit attributes. That is, the large value means better performance, such as the amount of production for a factory. J2 is a set of cost attributes. The smaller value means better performance, such as the number of employees for a factory. 5) Develop a distance measure over each criterion to both ideal (Dþ) and nadir (D)
Dþ i
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u bs ij Sþ ¼ t j
(12)
j
D i
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u bs ij S ¼ t j
(13)
j
6) Calculate relative closeness Di for each Pareto solution according to following equation:
Di ¼
D D þ Dþ
i ¼ 1; .; m
(14)
7) Choose the best compromise solution whose relative closeness Di is the closest to 1.
Fig. 6. CO2 vs. power in six-objective optimization.
6. Six-Objective optimization and using TOPSIS to determine the best trade-off solutions To investigate the optimal output in different conditions of engine variables (engine speed and blend percentage), six-objective optimization problems were solved. Power, BSFC, PM, NOx, CO and CO2 are chosen as objective functions for this multi-objective optimization process. This will allow finding trade-off optimum design points from the view point of all six-objective functions simultaneously. The feed forward neural network models got in section 3 are now deployed in these six-objective optimization problems. The optimization problem can be formulated in the following form:
8 Maximize > > > > Minimize > > > > Minimize > > < Minimize > Minimize > > > > Minimize > > > > 1000 Speed 2000 > : 0 Blend 50
f 1 ¼ Brake Power f 2 ¼ BSFC f 3 ¼ PM f 4 ¼ NOx f 5 ¼ CO f 6 ¼ CO2
(15)
A population of 80 individuals with a crossover probability of 0.6 and mutation probability of 0.08 was used in 400 generations for such 6-objective optimization problem.
Fig. 8. NOx vs. BSFC in six-objective optimization.
314
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
Fig. 9. CO vs. BSFC in six-objective optimization.
Fig. 10. CO2 vs. BSFC in six-objective optimization.
A total 1274 non-dominated optimum design points were gotten during optimization process. The non-dominated individuals of the six-objective optimization in the plane of power and BSFC together with the results of a separately run two-objective optimization of the same two objectives were depicted in Fig. 2. Such nondominated individuals of six and two-objective optimization were shown on the other planes in Figs. 3e10. It should be noted that there is a single set of individuals as a result of the six-objective optimization that are shown in different planes of objective
functions. Thus, there are some points in each plane that may dominate others in the same plane. However, these individuals are all non-dominated when considering all six objectives simultaneously. If the design variables (Engine speed and Biodiesel percent in blends) are selected, based on the Pareto sets, it leads to the best possible combination of those six objectives. Moreover, it can readily be observed that the results of such six-objective optimization include those of the two-objective optimization and, therefore, provide more optimal choices for the designer. Such an overlay graph in which the results of the independently got twoobjective optimization lie on the boundary of the six-objective optimization indeed exhibits the correctness of the Pareto frontiers. It is now desired to find a trade-off optimum design points out of all non-dominated six-objective optimization process compromising all objective functions. This can be achieved by TOPSIS method described in section 6. TOPSIS method is applied on the individuals obtained in six and some of two-objective optimization process separately. In this way, equal weights are used to consider non-preference for all objective functions. Consequently, optimum design point A is got by applying TOPSIS on the results of twoobjective optimization problems of power and BSFC. Similarly, considering conjugation of Power or BSFC with the emissions as objective functions and applying TOPSIS, optimum design points B to I are got. Finally TOPSIS is employed to get trade-off optimum point P from the six-objective optimization problem. Design points A to P are depicted in Figs. 2e10 and the values of design variables and objective functions for these points are depicted in Table 5. Optimum points J to O represented in Table 5 and Figs. 3e10 are the results of the single objective optimization which show the best values of each objective. It means that if someone looks for improve on only one of the six-objective functions, one of the points J to O. As it is expected, biodiesel percent reduction in blend to 0 and engine speed increase to about 2000 rpm, maximum power was achieved (See point K). Moreover, for gaining minimum NOx, engine speed was set to the lower bound (point L). Moreover, another trade-off design point Q can be simply recognized from Figs. 2e10. This point is closely near to the Pareto fronts in all planes and also has good power about 50 kW. This issue shows that it is worthy from the view point of all objective functions. Consequently, there are some important optimal design facts among the objective functions which discovered by the multiobjective optimization of the ANN meta-models obtained using the experimental analysis of the diesel engine. Such important
Table 5 The best compromise solution determined by TOPSIS.
Two-objective optimization process þ Topsis
Single objective optimization
Six-objective optimization process þ TOPSIS -
Point
Objectives
Speed (rpm)
Bio percent
Power (kW)
BSFC (g/kW-h)
CO2 (% Vol)
CO (% Vol)
NOx (ppm)
PM (mg/m3)
A B C D E F G H I J K L M N O P
Power-BSFC Power-PM Power-NOx Power-CO Power-CO2 BSFC-PM BSFC-NOx BSFC-CO BSFC-CO2 BSFC Power NOx PM CO CO2 6-objective
1000.0 1356.6 1000.2 1901.6 1917.4 1312.1 1000.2 1846.3 1858.5 1353.9 1996.1 1000.3 1299.4 1897.5 1969.6 1394.8
35.35 2.15 37.83 45.45 46.60 0.34 38.52 46.37 48.35 36.1 0 39.41 7.37 49.67 49.43 37.96
53.16 41.24 50.45 40.36 38.13 31.68 49.35 38.37 35.11 29.46 61 48.36 29.83 32.68 30.92 47.23
214.07 235.28 205.10 316.49 325.03 227.56 207.55 316.88 329.13 203.78 255.0 211.37 232.85 336.64 340.45 216.11
14.15 11.36 14.49 1.92 1.48 11.66 14.41 1.79 1.22 12.17 8.92 14.21 11.28 0.86 0.69 11.37
0.24 0.40 0.25 0.08 0.07 0.47 0.24 0.075 0.06 0.36 0.31 0.24 0.46 0.05 0.06 0.30
566 1363 383 1316 1429 1500 365 1381 1555 761 927 355 1539 1659 1662 580
601.15 0.84 600.01 58.56 62.47 8.00E-05 599.89 54.85 63.05 0.013 47.5 600.39 0.00003 62.25 67.80 27.79
Q
e
1831.3
35.894
67.02
249.0671
7.64429
0.21931
658
27.82
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
optimal design points could not be found without the multiobjective optimization approach of such diesel engine. 7. Conclusions Feed forward neural network approach was used successfully to derive models of the performance and emissions of the diesel engine fueled with castor oil biodiesel blends. The derived models were then used in an evolutionary multi-objective Pareto based optimization process so that some interesting and informative optimum design aspects revealed for the diesel engine with respect to the control variables of biodiesel percent and engine speed. For getting better results, common NSGA-II algorithm was modified. This optimization led to the discovering of some important tradeoff points among those objective functions. Such multi-objective optimization of diesel engine could unveil very important design trade-offs between conflicting objective functions which would not have been found otherwise. Furthermore, it was shown that the results of six-objective optimization include those of two-objective optimization in terms of Pareto frontiers and provide, accordingly, more choices for optimal design. Finally, some trade-off optimum design points were determined and presented by applying TOPSIS method on the non-dominated solutions obtained through six- and two-objective problems. Designers can use these points in the engine map for getting better performance. Acknowledgements The authors would like to acknowledge Iranian Fuel Conservation Company for supporting us in doing this research. References [1] A. Demirbas, Biodiesels e A Realistic Fuel Alternative for Diesel Engines, Springer, London, 2008. [2] G. Knothe, J.V. Gerpen, J. Krahl, The Biodiesel Handbook, AOCS Press, Illinois, 2005. [3] J. Starbuck, G.D.J. Harper, Run Your Diesel Vehicle on Biofuels, McGraw-Hill, New York, 2009. [4] B. Ghobadian, H. Rahimi, A.M. Nikbakht, G. Najafi, T.F. Yusaf, Diesel engine performance and exhaust emission analysis using waste cooking biodiesel fuel with an artificial neural network, Renew. Energy 34 (2009) 976e982. [5] M. Kiani Deh Kiani, B. Ghobadian, T. Tavakoli, A.M. Nikbakht, G. Najafi, Application of artificial neural networks for the prediction of performance and exhaust emissions in SI engine using ethanol-gasoline blends, Energy 35 (2010) 65e69.
315
[6] N. Kara Togun, S. Baysec, Prediction of torque and specific fuel consumption of a gasoline engine by using artificial neural networks, Appl. Energy 87 (2010) 349e355. [7] Shivakumar, P. Srinivasa Pai, B.R. Shrinivasa Rao, Artificial Neural Network based prediction of performance and emission characteristics of a variable compression ratio CI engine using WCO as a biodiesel at different injection timings, Appl. Energy 88 (2011) 2344e2354. [8] M. Gölcü, Y. Sekmen, P. Erduranlı, M. Sahir Salman, Artificial neural-network based modeling of variable valve-timing in a spark-ignition engine, Appl. Energy 81 (2005) 187e197. [9] S. Orçun Mert, Z. Özçelik, Y. Özçelik, I. Dinçer, Multi-objective optimization of a vehicular PEM fuel cell system, Appl. Thermal Eng. 31 (2011) 2171e2176. [10] P. Ahmadi, I. Dincer, Thermodynamic and exergoenvironmental analyses, and multi-objective optimization of a gas turbine power plant, Appl. Thermal Eng. 31 (2011) 2529e2540. [11] N. Srinivas, K. Deb, Multiobjective optimization using nondominated sorting in genetic algorithms, Int. J. Evol. Comput. 2 (1994) 221e248. [12] A. Jamali, N. Nariman-zadeh, A. Darvizeh, A. Masoumi, S. Hamrang, Multiobjective evolutionary optimization of polynomial neural networks for modelling and prediction of explosive cutting process, Int. J. Eng. Appl. Art Intel 22 (2009) 676e687. [13] A. Khalkhali, N. Nariman-zadeh, A. Darvizeh, A. Masoumi, B. Notghi, Reliability-based robust multi-objective crashworthiness optimisation of S-shaped box beams with parametric uncertainties, Int. J. Crashworth 15 (4) (2010) 443e456. [14] N. Nariman-Zadeh, M. Salehpour, A. Jamali, E. Haghgoo, Pareto optimization of a five-degree of freedom vehicle vibration model using a multi-objective uniform-diversity genetic algorithm (MUGA), Eng. Appl. Art Intel. 23 (2010) 543e551. [15] W.S. Lee, L.C. Lin, Evaluating and ranking the energy performance of office building using technique for order preference by similarity to ideal solution, Appl. Thermal Eng. 31 (2011) 3521e3525. [16] M. Boix, L. Pibouleau, L. Montastruc, C. Azzaro-Pantel, S. Domenech, Minimizing water and energy consumptions in water and heat exchange networks, Appl. Thermal Eng. 36 (2012) 442e455. [17] S. Haykin, Neural Networks: A Comprehensive Foundation, Mac-millan, New York, 1994. [18] Y. Çay, A. Çiçek, F. Kara, S. Sagiroglu, Prediction of engine performance for an alternative fuel using artificial neural network, Appl. Thermal Eng. 37 (2012) 217e225. [19] C.A. Coello Coello, A.D. Christiansen, Multiobjective optimization of trusses using genetic algorithms, Comp. Struct. 75 (2000) 647e660. [20] A. Osyezka, Multicriteria Optimization for Engineering Design, Design Optimization, Academic Press, NY, 1985, pp. 193e227. [21] C.M. Fonseca, P.J. Fleming, Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization, in: S. Forrest (Ed.), Proc.. of the Fifth Int. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1993, pp. 416e423. [22] C.A. Coello Coello, D.A. Van Veldhuizen, G.B. Lamont, Evolutionary Algorithms for Solving Multi-objective Problems, Kluwer Academic Publishers, NY, 2002. [23] V. Pareto, Cours d’economic ploitique, Rouge, Lausanne, Switzerland, 1896. [24] D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York, 1989. [25] A. Toffolo, E. Benini, Genetic diversity as an objective in multi-objective evolutionary algorithms, Evol Comput 11 (2) (2003) 151e167. [26] C.L. Hwang, K. Yoon, Multiple Attribute Decision Making e Methods and Applications, Springer-Verlag Press, Heidelberg, 1981.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
A hybrid method of modified NSGA-II and TOPSIS to optimize performance and emissions of a diesel engine using biodiesel Mir Majid Etghani a, *, Mohammad Hassan Shojaeefard b, Abolfazl Khalkhali b, Mostafa Akbari b a b
Mechanical Engineering Department, Islamic Azad University, Qaemshahr Branch, Mazandaran, Iran Automotive Engineering Department, Iran University of Science and Technology, Tehran, Iran
h i g h l i g h t s Effects of castor oil biodiesel blends have been examined on the diesel engine performance and emissions. Modeling engine performance and emissions by artificial neural network with back-propagation algorithm accurately. 2 and 6-objective optimization has been applied by the modified NSGA-II. Trade-off optimum design points are determined by applying TOPSIS.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 September 2012 Accepted 24 May 2013 Available online 3 June 2013
This paper addresses artificial neural network (ANN) modeling followed by multi-objective optimization process to determine optimum biodiesel blends and speed ranges of a diesel engine fueled with castor oil biodiesel (COB) blends. First, an ANN model was developed based on standard back-propagation algorithm to model and predict brake power, brake specific fuel consumption (BSFC) and the emissions of engine. In this way, multi-layer perception (MLP) network was used for non-linear mapping between the input and output parameters. Second, modified NSGA-II by incorporating diversity preserving mechanism called the ε-elimination algorithm was used for multi-objective optimization process. Six objectives, maximization of brake power and minimization of BSFC, PM, NOx, CO and CO2 were simultaneously considered in this step. Optimization procedure resulted in creating of non-dominated optimal points which gave an insight on the best operating conditions of the engine. Third, an approach based on TOPSIS method was used for finding the best compromise solution from the obtained set of Pareto solutions. 2013 Elsevier Ltd. All rights reserved.
Keywords: Performance Emissions Castor oil biodiesel ANN NSGA-II TOPSIS
1. Introduction Today caused by considerable growth of demands, known petroleum reserves are extremely diminishing and due to the environmental concerns for pollution from exhausted gases and demanding of greenhouse gas reduction, renewable and alternative fuels in the automotive fuel markets grew fast during the 21st century [1]. Since biodiesel has all the characteristics that an alternative fuel to petrodiesel should have such as technically feasible, economically competitive, environmentally acceptable, and easily available,
* Corresponding author. Tel.: þ98 9122393445; fax: þ98 2177240362. E-mail addresses: [email protected], [email protected] (M.M. Etghani), [email protected] (M.H. Shojaeefard), [email protected] (A. Khalkhali), [email protected] (M. Akbari). 1359-4311/$ e see front matter 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.05.041
therefore in the diesel engines, biodiesel is the best candidate as alternative for petroleum-based diesel fuels. Biodiesel is briefly defined as the monoalkyl esters of vegetable oils or animal fats. Biodiesel is an ecological, renewable and less polluting fuel, and therefore it is environmentally useful [2]. The usage of biodiesel does not require any changes in the fuel distribution infrastructure, and it is competitive with conventional diesel fuel. Furthermore, biodiesel biodegrades much more rapidly than diesel fuel. So, considerable environmental benefits are provided [3]. Because of experimentally determining the engine performance map for different operating conditions and biodiesel blends are time and money consuming, ANNs are used in recent studies. ANN as a computational modeling tool is employed widely to alleviate the burden of experimental testing. Recently, the application of ANN method to predict performance and emissions of internal combustion engines has gained significant success. Ghobadian et al. [4] modeled a diesel engine using waste cooking biodiesel fuel by
310
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
ANN. They considered engine speed, percentage of bio-fuel blend as the input variables and torque, BSFC, Hydrocarbon (HC) and Carbone Monoxide (CO) as the outputs. Kiani Deh Kiani et al. [5] used ANN to predict the performance and emissions from a spark ignition engine using ethanol-gasoline blends where they considered engine speed, engine speed and blend percentage as the input parameters and engine torque, power and exhaust emissions (CO, CO2, NOx and HC) of the engine as the output parameters. Kara Togun et al. [6] developed ANN to predict torque and BSFC of a gasoline engine in terms of spark advance, throttle position and engine speed. Shivakumar et al. [7] have used ANN for prediction of performance and emission characteristics of a CI engine using WCO. In their work, ANN modeling was used to predict BTE, BSEC, Texh, NOx, HC and Smoke. This technology was also used for modeling of valve timing in a SI engine [8]. Design of modern engines is driven by many competing criteria. Reduction of brake specific fuel consumption is common in the automotive industry to reduce the fuel consumption. Moreover, because of the environmental concerns, reduction of emissions is also significant. On the other hand, increasing the engine power is the important goal of engine designers. So, to consider all such criteria simultaneously, a complex multi-objective optimization problem (MOP) must be solved. Many different methods were proposed by previous researchers for solving MOPs [9,10]. Nondominated Sorting Genetic Algorithm (NSGA-II) proposed by Srinivas and Deb [11], which is Pareto based approaches is one of the efficient algorithms for solving MOPs. It generates a set of nondominated solutions (Pareto solutions), where a non-dominated solution performs better on at least one criterion than the other solutions. To improve NSGA-II, Nariman-Zadeh proposed modified NSGA-II which use ε-elimination algorithm rather than crowding factor [12]. This method is employed successfully in many recent studies [13,14]. After finding out the non-dominated points, it is desired to find some trade-off optimum points compromising objective functions. For this purpose, technique for ordering preferences by similarity to ideal solution (TOPSIS) can be used. TOPSIS is based on simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. Several numerical experiments show that NSGA-II determines the Pareto set and TOPSIS finds the best compromise solutions for different scenarios [15,16]. In the present study, optimal operating condition of a diesel engine fueled by biodiesel is extracted by an approach based on three steps. At the first step, a multi-layer perception (MLP) network is learned by experimental data to model and predict engine power, BSFC and emissions. Such ANN models are then employed in the multi-objective optimization process at the second step. In this way, modified NSGA-II by incorporating diversity preserving mechanism called the ε-elimination algorithm is used to
Table 1 Engine technical specifications. Bore stroke Number of cylinders Volume capacity Cycle Aspiration Combustion system Compression ration Max. power Fuel pump Governing Cooling Weight Length width height
100 mm 127 mm 4 3.99 L 4 Stroke Wastegated turbocharger Fast ram direct injection 17.25:1 61 kW in 2000 rpm Bosch rotary with Boost control Mechanical Water, belt driven water pump 265 Kg 678.7 mm 655 mm 748.5 mm
Fig. 1. Schematic diagram of experimental setup.
set up a multi-objective optimization framework for maximizing engine power, minimizing BSFC and emissions. At the last step, TOPSIS is used to find the best compromise solution. 2. Experimental methodology The experiments were performed on the agricultural direct injection compression engine with specifications given in Table 1. An eddy current dynamometer was used for gathering outputs of engine. The schematically prepared diagram of experimental setup is given in Fig. 1. The relative emission parameters from an online and accurately calibrated exhaust gas analyzer AVL DiCOM were recorded. The accuracies of the measured parameters and the uncertainties in the calculated parameters are given in Table 2. The experiments were carried out by using pure diesel, B5 (5% biodiesel þ 95% diesel), B10, B15, B20, B25 and B30 at full loads and various engine speeds (1200, 1400, 1600, 1700, 1800, 2000 rpm). All tests were completed without any modifications on the engine. The tests were carried out under steady-state condition. Before each test, the engine was warmed up with diesel fuel for about 15 min until the cooling water temperature was stabilized. Then brake power, BSFC, Nitrogen oxides (NOx), Carbone dioxide (CO2), CO and PM were measured. Each test was repeated three times and the results of the three repetitions were averaged. Some of the experimental results are reported in Table 3. 3. Modeling and prediction using artificial neural network (ANN) The main focus of this section is modeling and prediction of engine output using ANN based on experimental results. The backpropagation learning algorithm was used in feed forward with one hidden layer. Blend percentage and engine speed were considered
Table 2 The accuracies uncertainties in the results. Parameters
Accuracies
Load Speed Time CO CO2 NOx PM Calculated results Power BSFC
2 N.m 5 rpm 0.5% 0.01 % Vol 0.01 % Vol 1 ppm 1 mg/m3 Uncertainty 0.2% 0.22%
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315 Table 3 Samples of experimental results with input and output parameters. No.
1 2 6 7 10 11 12 25 26 27 28 29 30 37 38 39 40 41 42
Inputs
Outputs
Speed (rpm)
Blend (%)
Power (hp)
BSFC (g/kW-h)
PM (mg/m3)
NO (PPM)
CO (%)
CO2 (%)
1200 1400 2000 1200 1700 1800 2000 1200 1400 1600 1700 1800 2000 1200 1400 1600 1700 1800 2000
0 0 0 5 5 5 5 20 20 20 20 20 20 30 30 30 30 30 30
56 65 82 55 72 76.1 79.8 52 60 64.1 66.9 70.4 74.3 50.1 57.7 62.2 64 67.65 71.3
241.4 237.6 255.7 245.8 243.9 250.9 263.9 255.5 250.1 252.37 260.3 271.2 288.2 258.7 252.63 254.5 264.22 276.8 300.4
521.9 160.8 41.13 488.6 58.79 47.78 36.78 361 111 73.5 34.61 31.04 27.45 327 102 65.47 27.15 25.63 24.12
1380 1254 926 1396 1193 1081 970 1428 1364 1311 1258 1140 1022 1445 1409 1345 1281 1165 1050
0.43 0.37 0.31 0.42 0.322 0.312 0.302 0.32 0.29 0.28 0.27 0.262 0.255 0.28 0.27 0.265 0.26 0.25 0.24
12.4 11.4 8.9 12.2 9.7 9.1 8.5 11.5 9.1 8.5 8.15 7.9 7.64 10.8 8 7.49 7.38 7.3 7.21
as input layer components, while the Power, BSFC, PM, NOx, CO and CO2 were considered as output layer components of the ANNs. In the ANN model, 34 values of which 42 experiments were used for training the network and 8 values were selected randomly to test the performance of the trained network. The input layer neurons receive information from the outside environment and transmit them to the neurons of the hidden layer without performing any calculation. The hidden layer neurons then process the incoming information and extract useful features to reconstruct the mapping from the input space. The neighboring layers are fully interconnected by weights. Finally, the output layer neurons produce the network prediction to the outside world [17]. One of the most important tasks in ANN studies is to determine the optimal network architecture which is related to hidden layers and neurons in it. Generally, the trial-and-error approach is used. In this study, the best architecture of the network was obtained by trying different hidden layers and neurons. The trial started on hidden layer with ten neurons, and the performance of each network was checked by three standard criteria, R, RMSE and MAPE (R is the correlation coefficient, RMSE is the root mean square error, and MRE is the mean relative error). These criteria are defined as following equations respectively:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 ! P u u j tj oj R ¼ t1 P 2 j oj
¼
¼
ð1=pÞ
X 1=2 tj oj 2
! p 1 X tj oj 100 tj p 1
311
representing inputs, neurons in hidden layers, and outputs, respectively. Table 4 shows its criteria. The learning algorithm used in the study is LevenbergeMarquardt (LM), activation function is logistic sigmoid (logsig) transfer functions and epoch numbers is 20,000. 4. Multi-objective optimization Multi-objective optimization, which is also called multi criteria optimization or vector optimization, defined as finding a vector of decision variables satisfying constraints to give acceptable values to all objective functions [19,20]. In these problems, there are several objectives or cost functions (a vector of objectives) to be optimized (minimized or maximized) simultaneously. These objectives often conflict with each other so that improving one of them will deteriorate another. Thus, there is no single optimal solution as the best with respect to all the objective functions. Instead, there is a set of optimal solutions, known as Pareto optimal solutions or Pareto front [21e25] for multi-objective optimization problems. The concept of Pareto front or set of optimal solutions in the space of objective functions in MOPs stands for a set of solutions that are non-dominated to each other but are superior to the rest of solutions in the search space. This means that it is not possible to find a single solution to be superior to all other solutions with respect to all objectives so that changing the vector of design variables in such a Pareto front consisting of these non-dominated solutions could not lead to the improvement of all objectives simultaneously. Therefore, such a change will lead to deteriorating of at least one objective. Thus, each solution of the Pareto set includes at least one objective inferior to that of another solution in that Pareto set, although both are superior to others in the rest of search space. Such problems can be mathematically defined as: Find the vector X * ¼ ½x*1 ; x*2 ; .; x*n to optimize
FðXÞ ¼ ½f1 ðXÞ; f2 ðXÞ; .; fk ðXÞT
(4)
subject to m inequality constraints
gi ðXÞ 0;
i ¼ 1 to m
(5)
and p equality constraints
hj ðXÞ ¼ 0;
j ¼ 1 to p
(6)
(2)
where X * ˛
(3)
Table 4 Three standard criteria obtained from the ANN.
(1)
R
where t is the target value, o is the output value and p is the pattern number [18]. The goal is to maximize correlation coefficient to obtain a network with the best generalization. Many different network models were tried and their R, RMSE and MAPE values were calculated. Based on this analysis, the optimal architecture of the ANN was constructed as 2e15e6 neural network architecture
Power BSFC PM NOx CO CO2
RMSE
MAPE
Train
Test
Train
Test
Train
Test
0.999995 0.999998 0.999995 0.999996 0.999978 0.999983
0.999956 0.999957 0.996709 0.999955 0.999937 0.999931
0.000772 0.001158 0.000719 0.001303 0.001472 0.001968
0.002223 0.0047 0.008131 0.004254 0.002437 0.003807
0.216595 0.12151 0.733854 0.169048 0.396388 0.350319
0.532047 0.51145 4.15107 0.538951 0.664076 0.685741
312
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
ci ¼ f1; 2; .; kg, ui vi ^ dj˛f1; 2; .; kg : ui < vi. In other words, there is at least one uj which is smaller than vj whilst the remaining u’s are either smaller or equal to corresponding v’s. A point X * ˛U (U is a feasible region in
Fig. 2. BSFC vs. power in six-objective optimization.
Fig. 3. NOx vs. power in six-objective optimization.
objective weights. The TOPSIS process for determining the best compromise solution is briefly presented as follows: 1) Input matrix S, where the element sij is the jth objective value of the ith alternative (that is, S is composed of the Pareto solutions) 2) Calculate normalized rating ~sij according to the following equation:
sij ~sij ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pm 2ffi i¼1 sij
i ¼ 1; .; m; j ¼ 1; .; n
(7)
3) Construct the weighted normalized values bs ij using the following equation:
b s ij ¼ wj ~sij
i ¼ 1; .; m; j ¼ 1; .; n
(8)
where wj is the weight value of jth attribute and must satisfy: n X
wj ¼ 1
(9)
j¼1
4) Determine Sþ and S as follow:
Sþ ¼ S ¼
maxb s ij jj˛J1 ; minb s ij jj˛J2 ;
i ¼ 1; 2; .; m
(10)
minb s ij jj˛J1 ; maxb s ij jj˛J2 ;
i ¼ 1; 2; .; m
(11)
Fig. 4. PM vs. power in six-objective optimization.
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
313
Fig. 5. CO vs. power in six-objective optimization.
Fig. 7. PM vs. BSFC in six-objective optimization.
where J1 is a set of benefit attributes. That is, the large value means better performance, such as the amount of production for a factory. J2 is a set of cost attributes. The smaller value means better performance, such as the number of employees for a factory. 5) Develop a distance measure over each criterion to both ideal (Dþ) and nadir (D)
Dþ i
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u bs ij Sþ ¼ t j
(12)
j
D i
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u bs ij S ¼ t j
(13)
j
6) Calculate relative closeness Di for each Pareto solution according to following equation:
Di ¼
D D þ Dþ
i ¼ 1; .; m
(14)
7) Choose the best compromise solution whose relative closeness Di is the closest to 1.
Fig. 6. CO2 vs. power in six-objective optimization.
6. Six-Objective optimization and using TOPSIS to determine the best trade-off solutions To investigate the optimal output in different conditions of engine variables (engine speed and blend percentage), six-objective optimization problems were solved. Power, BSFC, PM, NOx, CO and CO2 are chosen as objective functions for this multi-objective optimization process. This will allow finding trade-off optimum design points from the view point of all six-objective functions simultaneously. The feed forward neural network models got in section 3 are now deployed in these six-objective optimization problems. The optimization problem can be formulated in the following form:
8 Maximize > > > > Minimize > > > > Minimize > > < Minimize > Minimize > > > > Minimize > > > > 1000 Speed 2000 > : 0 Blend 50
f 1 ¼ Brake Power f 2 ¼ BSFC f 3 ¼ PM f 4 ¼ NOx f 5 ¼ CO f 6 ¼ CO2
(15)
A population of 80 individuals with a crossover probability of 0.6 and mutation probability of 0.08 was used in 400 generations for such 6-objective optimization problem.
Fig. 8. NOx vs. BSFC in six-objective optimization.
314
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
Fig. 9. CO vs. BSFC in six-objective optimization.
Fig. 10. CO2 vs. BSFC in six-objective optimization.
A total 1274 non-dominated optimum design points were gotten during optimization process. The non-dominated individuals of the six-objective optimization in the plane of power and BSFC together with the results of a separately run two-objective optimization of the same two objectives were depicted in Fig. 2. Such nondominated individuals of six and two-objective optimization were shown on the other planes in Figs. 3e10. It should be noted that there is a single set of individuals as a result of the six-objective optimization that are shown in different planes of objective
functions. Thus, there are some points in each plane that may dominate others in the same plane. However, these individuals are all non-dominated when considering all six objectives simultaneously. If the design variables (Engine speed and Biodiesel percent in blends) are selected, based on the Pareto sets, it leads to the best possible combination of those six objectives. Moreover, it can readily be observed that the results of such six-objective optimization include those of the two-objective optimization and, therefore, provide more optimal choices for the designer. Such an overlay graph in which the results of the independently got twoobjective optimization lie on the boundary of the six-objective optimization indeed exhibits the correctness of the Pareto frontiers. It is now desired to find a trade-off optimum design points out of all non-dominated six-objective optimization process compromising all objective functions. This can be achieved by TOPSIS method described in section 6. TOPSIS method is applied on the individuals obtained in six and some of two-objective optimization process separately. In this way, equal weights are used to consider non-preference for all objective functions. Consequently, optimum design point A is got by applying TOPSIS on the results of twoobjective optimization problems of power and BSFC. Similarly, considering conjugation of Power or BSFC with the emissions as objective functions and applying TOPSIS, optimum design points B to I are got. Finally TOPSIS is employed to get trade-off optimum point P from the six-objective optimization problem. Design points A to P are depicted in Figs. 2e10 and the values of design variables and objective functions for these points are depicted in Table 5. Optimum points J to O represented in Table 5 and Figs. 3e10 are the results of the single objective optimization which show the best values of each objective. It means that if someone looks for improve on only one of the six-objective functions, one of the points J to O. As it is expected, biodiesel percent reduction in blend to 0 and engine speed increase to about 2000 rpm, maximum power was achieved (See point K). Moreover, for gaining minimum NOx, engine speed was set to the lower bound (point L). Moreover, another trade-off design point Q can be simply recognized from Figs. 2e10. This point is closely near to the Pareto fronts in all planes and also has good power about 50 kW. This issue shows that it is worthy from the view point of all objective functions. Consequently, there are some important optimal design facts among the objective functions which discovered by the multiobjective optimization of the ANN meta-models obtained using the experimental analysis of the diesel engine. Such important
Table 5 The best compromise solution determined by TOPSIS.
Two-objective optimization process þ Topsis
Single objective optimization
Six-objective optimization process þ TOPSIS -
Point
Objectives
Speed (rpm)
Bio percent
Power (kW)
BSFC (g/kW-h)
CO2 (% Vol)
CO (% Vol)
NOx (ppm)
PM (mg/m3)
A B C D E F G H I J K L M N O P
Power-BSFC Power-PM Power-NOx Power-CO Power-CO2 BSFC-PM BSFC-NOx BSFC-CO BSFC-CO2 BSFC Power NOx PM CO CO2 6-objective
1000.0 1356.6 1000.2 1901.6 1917.4 1312.1 1000.2 1846.3 1858.5 1353.9 1996.1 1000.3 1299.4 1897.5 1969.6 1394.8
35.35 2.15 37.83 45.45 46.60 0.34 38.52 46.37 48.35 36.1 0 39.41 7.37 49.67 49.43 37.96
53.16 41.24 50.45 40.36 38.13 31.68 49.35 38.37 35.11 29.46 61 48.36 29.83 32.68 30.92 47.23
214.07 235.28 205.10 316.49 325.03 227.56 207.55 316.88 329.13 203.78 255.0 211.37 232.85 336.64 340.45 216.11
14.15 11.36 14.49 1.92 1.48 11.66 14.41 1.79 1.22 12.17 8.92 14.21 11.28 0.86 0.69 11.37
0.24 0.40 0.25 0.08 0.07 0.47 0.24 0.075 0.06 0.36 0.31 0.24 0.46 0.05 0.06 0.30
566 1363 383 1316 1429 1500 365 1381 1555 761 927 355 1539 1659 1662 580
601.15 0.84 600.01 58.56 62.47 8.00E-05 599.89 54.85 63.05 0.013 47.5 600.39 0.00003 62.25 67.80 27.79
Q
e
1831.3
35.894
67.02
249.0671
7.64429
0.21931
658
27.82
M.M. Etghani et al. / Applied Thermal Engineering 59 (2013) 309e315
optimal design points could not be found without the multiobjective optimization approach of such diesel engine. 7. Conclusions Feed forward neural network approach was used successfully to derive models of the performance and emissions of the diesel engine fueled with castor oil biodiesel blends. The derived models were then used in an evolutionary multi-objective Pareto based optimization process so that some interesting and informative optimum design aspects revealed for the diesel engine with respect to the control variables of biodiesel percent and engine speed. For getting better results, common NSGA-II algorithm was modified. This optimization led to the discovering of some important tradeoff points among those objective functions. Such multi-objective optimization of diesel engine could unveil very important design trade-offs between conflicting objective functions which would not have been found otherwise. Furthermore, it was shown that the results of six-objective optimization include those of two-objective optimization in terms of Pareto frontiers and provide, accordingly, more choices for optimal design. Finally, some trade-off optimum design points were determined and presented by applying TOPSIS method on the non-dominated solutions obtained through six- and two-objective problems. Designers can use these points in the engine map for getting better performance. Acknowledgements The authors would like to acknowledge Iranian Fuel Conservation Company for supporting us in doing this research. References [1] A. Demirbas, Biodiesels e A Realistic Fuel Alternative for Diesel Engines, Springer, London, 2008. [2] G. Knothe, J.V. Gerpen, J. Krahl, The Biodiesel Handbook, AOCS Press, Illinois, 2005. [3] J. Starbuck, G.D.J. Harper, Run Your Diesel Vehicle on Biofuels, McGraw-Hill, New York, 2009. [4] B. Ghobadian, H. Rahimi, A.M. Nikbakht, G. Najafi, T.F. Yusaf, Diesel engine performance and exhaust emission analysis using waste cooking biodiesel fuel with an artificial neural network, Renew. Energy 34 (2009) 976e982. [5] M. Kiani Deh Kiani, B. Ghobadian, T. Tavakoli, A.M. Nikbakht, G. Najafi, Application of artificial neural networks for the prediction of performance and exhaust emissions in SI engine using ethanol-gasoline blends, Energy 35 (2010) 65e69.
315
[6] N. Kara Togun, S. Baysec, Prediction of torque and specific fuel consumption of a gasoline engine by using artificial neural networks, Appl. Energy 87 (2010) 349e355. [7] Shivakumar, P. Srinivasa Pai, B.R. Shrinivasa Rao, Artificial Neural Network based prediction of performance and emission characteristics of a variable compression ratio CI engine using WCO as a biodiesel at different injection timings, Appl. Energy 88 (2011) 2344e2354. [8] M. Gölcü, Y. Sekmen, P. Erduranlı, M. Sahir Salman, Artificial neural-network based modeling of variable valve-timing in a spark-ignition engine, Appl. Energy 81 (2005) 187e197. [9] S. Orçun Mert, Z. Özçelik, Y. Özçelik, I. Dinçer, Multi-objective optimization of a vehicular PEM fuel cell system, Appl. Thermal Eng. 31 (2011) 2171e2176. [10] P. Ahmadi, I. Dincer, Thermodynamic and exergoenvironmental analyses, and multi-objective optimization of a gas turbine power plant, Appl. Thermal Eng. 31 (2011) 2529e2540. [11] N. Srinivas, K. Deb, Multiobjective optimization using nondominated sorting in genetic algorithms, Int. J. Evol. Comput. 2 (1994) 221e248. [12] A. Jamali, N. Nariman-zadeh, A. Darvizeh, A. Masoumi, S. Hamrang, Multiobjective evolutionary optimization of polynomial neural networks for modelling and prediction of explosive cutting process, Int. J. Eng. Appl. Art Intel 22 (2009) 676e687. [13] A. Khalkhali, N. Nariman-zadeh, A. Darvizeh, A. Masoumi, B. Notghi, Reliability-based robust multi-objective crashworthiness optimisation of S-shaped box beams with parametric uncertainties, Int. J. Crashworth 15 (4) (2010) 443e456. [14] N. Nariman-Zadeh, M. Salehpour, A. Jamali, E. Haghgoo, Pareto optimization of a five-degree of freedom vehicle vibration model using a multi-objective uniform-diversity genetic algorithm (MUGA), Eng. Appl. Art Intel. 23 (2010) 543e551. [15] W.S. Lee, L.C. Lin, Evaluating and ranking the energy performance of office building using technique for order preference by similarity to ideal solution, Appl. Thermal Eng. 31 (2011) 3521e3525. [16] M. Boix, L. Pibouleau, L. Montastruc, C. Azzaro-Pantel, S. Domenech, Minimizing water and energy consumptions in water and heat exchange networks, Appl. Thermal Eng. 36 (2012) 442e455. [17] S. Haykin, Neural Networks: A Comprehensive Foundation, Mac-millan, New York, 1994. [18] Y. Çay, A. Çiçek, F. Kara, S. Sagiroglu, Prediction of engine performance for an alternative fuel using artificial neural network, Appl. Thermal Eng. 37 (2012) 217e225. [19] C.A. Coello Coello, A.D. Christiansen, Multiobjective optimization of trusses using genetic algorithms, Comp. Struct. 75 (2000) 647e660. [20] A. Osyezka, Multicriteria Optimization for Engineering Design, Design Optimization, Academic Press, NY, 1985, pp. 193e227. [21] C.M. Fonseca, P.J. Fleming, Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization, in: S. Forrest (Ed.), Proc.. of the Fifth Int. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1993, pp. 416e423. [22] C.A. Coello Coello, D.A. Van Veldhuizen, G.B. Lamont, Evolutionary Algorithms for Solving Multi-objective Problems, Kluwer Academic Publishers, NY, 2002. [23] V. Pareto, Cours d’economic ploitique, Rouge, Lausanne, Switzerland, 1896. [24] D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York, 1989. [25] A. Toffolo, E. Benini, Genetic diversity as an objective in multi-objective evolutionary algorithms, Evol Comput 11 (2) (2003) 151e167. [26] C.L. Hwang, K. Yoon, Multiple Attribute Decision Making e Methods and Applications, Springer-Verlag Press, Heidelberg, 1981.